Critical Speed and Limit Speed in Phenomena of Lateral Instability on Railway Vehicles

A comparison between theoretical calculations on dynamic lateral behaviour of railway vehicles and experimental results shows quite a sizeable difference between the calculated critical speed and the actual speed at which side impact phenomena will repeatedly occur between wheel flange and rail (running speed limit), such impact speed being remarkably lower than calculated.

Another typical experimental aspect is that the running speed limit will considerably vary for the same vehicle depending on the test track conditions. Such difference is usually attributed to alterations of the wheel-rail contact surfaces, only.

This paper will discuss some concurrent causes which may prove far from negligible, such as the effects of track defects, an amplification of the dynamic lateral displacement between wheel and rail on approaching the critical speed, the track mechanical properties, and in particular the track lateral rigidity.

The influence of some geometrical factors typical of the wheel-rail contact, such as side clearance and linearized conicity, will also be discussed. The approach is based on the application of statistical methods to dynamic linear systems.     

Dynamic Interaction of Railway Systems with Large Bridges

In this paper have been described

- railway runability problems on large span bridges;

- the state-of-art of the methodologies adopted for a systematic analysis of the dynamic behaviour of railway vehicles running on a deformable structure, with particular reference to large span suspension bridges;

- some meaningful experimental and analytical results, related to railway runability of large span bridges.     

A Modular Computer Model for the Design of Vehicle Dynamics Control Systems1

This paper describes a multiport approach to computer-aided modeling of vehicle dynamics. The modeling approach produces models that are suitable for the interactive design and evaluation of complex control strategies. The vehicle model which can be used for ride and handling analysis, is built from modular components. The components are programmed using the syntax of the computer aided control system design (CACSD) program EASYS. Seven modeling components are used to create a three-dimensional vehicle dvnamics model. The model is flexible enoug-h to simulate any suspension design with revolute joints.

Each component of the model consists of a FORTRAN subroutine and a main calling module called a macro. To simplify the process of model building, the modeling components in the car model are designed to represent physical elements, such as the spring, damper, link or tire. To create a model, the components, which are represented by blocks, are interconnected through points, located on the blocks, called pons. These ports have been designed to simulate the location of the connection points between the physical elements, as observed in real systems. The construction of multibody models within a CACSD program offers the flexibility of simultaneous interactive simulation of the three-dimensional dvnamics and evaluation of the desien of the controls.

Although modeling of multibody systems using FORTRAN components has been pioneered by Chace, Haug and Orlandea; and bond graph modeling of multibody systems has been investigated by Bos, this approach is novel because:-

The model is included in the control system design program (EASYS). This arrangement allows the designer to exploit the advanced control design tools available in the program. Furthermore, this approach significantly reduces the computation time required for running the model after parameters modification.

The model is built from components that are interconnected by ports which represent the actual physical location of the connection points between the elements. The multiport approach simplifies the model building process for multibody systems. This simplification is achieved by reducing the model of a multibody system to a block diagram form.     

Seat Movement Relative to the Passenger Compartment—A Possible Method to Improve Passenger Protection During Frontal Impacts

The present study is meant to prove in a theoretical way that a controlled seat movement relative to the passenger compartment will result into an improvement of passenger deceleration during vehicle frontal impacts.

This effect could be of advantage in some respects: as possible alternative for the most favourable design of the energy absorbing zones of a vehicle, as an additional safety device for the occupants of heavy vehicles with relatively soft impact absorbing zones in case of crashes against rigid obstacles, and in small vehicles where only little space exists for passenger protection.

With regard to the complexity of this subject, the study at hand must be regarded as a first step towards the final solution of the problem.     

Dynamic Behaviour of Ore Wagons in Curves at Malmbanan

The transportation of ore can be made more cost efficient by use of bigger and heavier trains. An increase in axle load is thereby wanted. The fleet of ore wagons of today at Malmbanan/Ofotbanan in northern Sweden and Norway has to be updated. It is of interest to find out if it is possible to allow a higher axle load on the track with new wagons

To be able to understand and predict the effects on track wear depending on what type of vehicle that is in use, the contact forces between wheels and rails have to be determined. A computer aided analysis has been made of the dynamic behaviour of three test vehicles equipped with different types of three-piece bogies running at Malmbanan. The vehicles are modelled and their interaction with the track is analysed using the multibody simulation package GENSYS

The simulations show that, even if the axle load is increased from 25 tons to 30 tons and the velocity is increased from 50 km/h to 60 km/h, it is possible to reduce lateral track forces and wear in curves by using a different bogie than the standard three-piece bogie used today.     

The Lateral Dynamics of Motorcycles and Bicycles

The paper is a review of the state of knowledge and understanding of the steering behaviour of single-track vehicles, with the main accent on vehicle design, and vehicle design analysis and behaviour prediction.

The body of the paper consists of a chronological account of the steps which have been taken in establishing the current position. Scientific study of the motions of two-wheelers has been in progress for more than 100 years, but progress was slow and many conflicting conclusions were drawn until increasing understanding of tyre mechanics, systematic application of the laws of motion for systems of rigid bodies, digital computation and modern numerical methods, and improved mobile measurement, recording, and data processing capabilities allowed the pace to accelerate.

The current position, which is that a good understanding of the relationship between design and performance has been achieved, but that by no means have all the problems of significance been solved, is described at the end of the paper.     

Messungen von Fahrbahn-Unebenheiten paralleler Fahrspuren und Anwendung der Ergebnisse

Measurement of two track road inputs and theoretical application of the results

The calculation of vehicle response to road-surface irregularity inputs requires the spectral densities of the left and right longitudinal track and their statistical dependence

This paper presents some resluts of parallel profile measurements, three typical german roads have been chosen

Random vibration of two vehicle types are digital-simulated. The dynamic tire load shows that independent suspension systems are more advantageous than beam axles, because by wheel tramp this type increases the dynamic tire load.     

Longitudinal Oscillations of Vehicle/Trailer Combinations Induced by Overrun Braking

A mathematical model for the representation of longitudinal oscillations which can occur in car/trailer systems in braking, when the trailer brakes are applied through compression of the towing hitch, is described. The model is used to show how the trailer braking system parameters affect the steady deceleration performance of the vehicle combination, and the stability, in the linear system sense, of the steady motions. The sensitivity of the stability to other system design parameters is also examined.

Digital simulation of the motions occurring in response to a step input of car braking torque is reported, with the results confirming the predictions of the linear stability analysis, and also showing the influence of backlash in the trailer brake actuating mechanism.

The system is shown to be capable of self-excitation in a “shunting” mode, in which the car and trailer motions are in antiphase, with the stability/damping property critically dependent on drawbar damping, and only weakly dependent on other system parameters. The characteristic frequency of the “shunting” mode oscillations is shown to be controllable via the stiffness of the trailer brake linkage, but this frequency is closely related to the steady drawbar deflection which occurs in uniform deceleration.

The model behaviour described provides a basis for the design of relevant systems whose longitudinal dynamic characteristics will be satisfactory.     

Very-High-Speed Tests on the French Railway Track

The very-high-speed tests carried out by SNCF between the end of 1989 and May 1990, are an extension of the investigations which have been made for many years in order to acquire the control of high speeds. The high-speed run which ended the tests is well known [1], [2],[3].

In order to place the final test campaign in its context, we can recall progression made during the last decade.

In February 1981, the maximal speed of 380 km/h was reached with a TGV-PSE¹ train set, having the same configuration as the series, but only seven trailers instead of eight.

During the following years, until 1986, the pneumatic suspension and the new Y 231 carrying bogies designed for TGV-ATL train sets were developed, with numerous test runnings in the speed range from 300 to 350 km/h, in order to obtain certitudes as regards the stability of the bogies and the appropriate choice of anti-hunting devices for commercial speeds of 270 km/h (LGV-PSE) or 300 km/h (LGV-ATL).

These tests allowed the definition of the TGV equipment design principles, which are applied today as regards the critical speed of the bogies.

Between 1985 and 1988, the development of the prototype train set equiped with self-controlled synchronous motors (March 1988) led once more to numerous runnings at high speed, in December 1988 with the so-called “operation TGV 88”. During this operation, the speed range from 350 to 400 km/h was investigated (maximal speed 408,4 km/h on December 12th 1988).

Apart from the capability of the synchronous traction equipment to develop the required power and the performance consisting in the realization of such tests on a line kept in operation (LGV-PSE), the teachings gathered together during this test campaign were decisive for the pursuit of the operation.

On this occasion, we discovered that:

-with the single-phase GPU pantograph mounted on this train set, we could get the current collection under control without difficulties inside the studied speed range,

-the bogies presented a stability margin distinctly higher than that which had been estimated, according to the results of former experiences.

Consequently, the test campaign of the TGV 117 could be engaged with a great confidence in the capabilities of the TGV equipment to achieve markedly higher speeds with full safety. The preparation of this test campaign had begun in 1986 and was conducted in a parallel direction to the above mentioned experimentation.

The campaign was preceded by a preliminary test campaign with the train set TGV-ATL n° 308, with a reduced train composition, including eight trailers. The goal was the validation, until 390 km/ h, of the test field consisting in the TGV-ATL Aquitaine branch, as well for the track as for the overhead contact line, the achievement of which was just ended.

The operation TGV 117 was then carried out in two phases:

-in December 1989 the train set TGV-ATL 325 with a reduced train composition consisting in four trailers between two motor cars reached the maximal speed of 482,4 km/h on December 5th,

-in May 1990 the same train set, but with only three trailers, improved the performance unto the final record: the speed of 515,3 km/h was reached on May 18th.     

Active Suspension Control; Performance Comparisons Using Control Laws Applied to a Full Vehicle Model

Based on a mathematical model of an actively suspended vehicle, the effects of the following issues in deriving the control laws are studied:

(a)representation of the ground surface as integrated or filtered white noise.

(b)cross-correlation between left and right track inputs.

(c)wheelbase time delay between front and rear inputs.

The third of these issues is shown to be by far the most important. Considerable improvements at the rear suspension can be obtained if the control law includes the information that the rear input is simply a delayed version of the front input. Effectively this provides feedforward terms in the control law for the rear actuator. For the full state feedback case, these improvements are indicated by reductions in the rear body acceleration and rear dynamic tyre load of around 20% and 40% respectively with no increase in suspension working space.     

Solution of the Multiple Wheel and Rail Contact Dynamic Problem

An unconventional method for calculating the forces developing in the wheel and rail contact patches of a railway vehicle has been implemented at the New Technology Laboratory of INRETS. It takes into account the elastic deformations of the materials in the Hertzian elliptical contact areas; the possibility of having simultaneously several contact patches on each wheel, is introduced in the simulation of the dynamic phenomena.

The theory is applied for a high speed bogie running on a perfectly straight track.     

Optimization for Vehicle Suspension II: Frequency Domain

The objective of this study is optimizing the components design of a vehicle suspension system under excitation due to road roughness. The vehicle is modelled as a dynamic system made of masses interconnected by, linear, springs and dampers. The optimizing code provides values corresponding to the caracteristics of masses, dampers and springs which, within a range, minimize the objective function for a defined excitation. This objective function auantifies the vehicle comfort level.

The optimization method used is the sequential linear programming by iteratively applying the Simplex algorithm. The model response is obtained in frequency domain and the vehicle excitation can be either random or deterministic.

The exact nature of the optimization problem, objective function and restrictions, depend on the type of excitation considered.

In succeeding paragraphs, the problem formulation together with a comparison with other authors is presented.     

Simulation and Visualisation of the Dynamic Behaviour of an Overhead Power System with Contact Breaking

For high speed rail traffic it is necessary to design overhead power systems which minimize the contact loss between pantograph head and contact wire. To predict how different design solutions will behave it is favourable to model and simulate the dynamic behaviour. In this paper a model of an overhead power system is specified and used in simulation. The model is suitable for simulation with contact loss since it includes specifications of impact conditions between pantograph head and contact wire. Two sets of equations of motion are specified, one for the contact case and one for the non-contact case. The model also includes lateral movement of the wire due to the zigzag span and friction between the pantograph head and the contact wire. It is shown how to make animations of the system behaviour using a MCAE-system. The animations are made using a geometrical model of the system together with results from numerical simulations.

Through the examples provided, use of the mathematical model and the geometrical model is presented. The response is visualised as time histories and phase plane diagrams of different coordinates and as animations of the total system response. The different types of visualisations make an excellent combination when studying the system behaviour of different design solutions.

In one example, simulation using the linearised set of equations gives the same results as simulation using the set of fully nonlinear equations, due to periodic response and the simple alternation of contact conditions. It is shown that the situation when any of the parameters vary suddenly is possible to simulate using the fully nonlinear equations of motion.     

Autonomous Lateral Control of Vehicles in an Automated Highway System

Lateral control of vehicles in IVHS requires the installation of on-board sensors as well as the installation of roadway hardware such as cables, magnets, etc. Existing control approaches in PATH require road curvature and vehicle lateral position (with respect to the center of the lane) information. Hence these approaches rely on roadway sensors to obtain relative lateral position. These methods will necessitate infrastructural changes to the highway.

This paper introduces the concept of autonomous lateral control or auto-tracking. The method allows us to use only line-of-sight sensor information to effect vehicle control. We present a detailed vehicle model. Controllers have been proposed to demonstrate the effectiveness of the proposed auto-tracking scheme. We also examine the possibilities of using this method for lane change purposes in an automated highway system.     

Dynasim 3: A Computer Program for Simulation Of Vehicle Riding Motions

The purpose of this paper is to present analytical techniques for evaluating the dynamic riding behaviour of a vehicle. These techniques have been applied to a fairly sophisticated model of a bus, where a three-dimensional structure, elastic frame and non-linear shock-absorbers have been considered.

A computer simulation program (DYNASIM 3) has been set up, which is actually used at FIAT corporation for evaluating vehicle riding qualities and improving the design process.     

Linearization Function of a Complex Nonlinear Two-Force-Element

Output force of a nonlinear two-force-element (TFE) excited by a stationary random process is stationary random as well and is described by its autocorrelation function.

Dependence of this autocorrelation function on the autocorrelation functions of the excitation process and of its velocity and on their crosscovanance function is indicated by the linearization (describing) function.

This paper describes the determination of the linearization function for a complex TFE composed of a parallel spring and damper, both having characteristics described by polynosmial functions. Knowledge of the linearization function is necessary for carrying out the second order linearization procedure of nonlinear dynamic systems excited by stationary random processes described in '1', '2', '3'.     

Dynamic Behaviour of a Mobile Robot Vehicle with a Two Caster and Two Driving Wheel Configuration

The actual trajectory covered by a mobile robot in motion differs from the trajectory planned on the basis of the kinematic characteristics of its directional control system. This difference is essentially related to the behaviour of wheel-road contact, the influence of dynamic loads and the presence of caster wheels.

This paper presents a mathematical model (“ DDPP) which simulates the motion of a generic mobile robot vehicle with a propulsion and directional control system based on two independent driving wheels and two caster wheels.

The differential equations of motion have been obtained by applying modified equations of Lagrange.

The role played by the dynamic loads, the wheel-road contact features and the caster wheels is discussed hereof.     

Optimization for Vehicle Suspension I: Time Domain

A numerical procedure for finding the optimum values of a number of parameters describing a model vehicle suspension has been studied. The vehicle has been modelled by dynamic systems of linear springs and dampers, and the goal is to obtain lower acceleration peaks at an elected design point in the vehicle.

The problem is stated as a mathematical programming problem which can be solved by means of the sequential linear programming technique. The procedure has been implemented for a four wheel independent suspension model capable of being subjected to road irregularities and to centrifugal and braking accelerations.     

The Influence of Structural Flexibilities on the Straight-running Stability of Motorcycles

A new tyre model for studies of motorcycle lateral dynamics, and three new motorcycle models, each incorporating a different form of structural compliance, are developed. The tyre model is based on “taut string” ideas, and includes consideration of tread width and longitudinal tread rubber distortion and tread mass effects, and normal load variation. Parameter values appropriate to a typical motorcycle tyre are employed. The motorcycle models are for small lateral perturbations from straight running at constant speed, and include (a) lateral compliance of the front wheel in the front forks, (b) torsional compliance of the front forks, and (c) torsional compliance in the rear frame at the steering head about an axis perpendicular to the steering axis.

Results in the form of eigenvalues, indicating modal damping properties and natural frequencies are presented for each model. The properties of four large production machines for a range of forward speeds, and the practicable range of stiffnesses are calculated, and the implications are discussed.

It is concluded that typical levels of structural compliance in models (a) and (c) contribute significantly to the steering behaviour properties of large motorcycles, and their observed behaviour can be understood better in terms of the new results than of those existing previously. Some conclusions relating to optimal structural stiffness properties are also drawn.